As a crucial part of a precast concrete segmental bridge system, connection joints should ensure shear force propagation due to the loading application from the bridge’s deck to the section below. In this study, double L-shaped concrete blocks connected by a steel shear key with epoxy are numerically simulated using Midas FEA to represent the precast concrete segmental bridge connections. The L-shaped concrete blocks are loaded in two directions, vertical load, which represents the deck load, while horizontal load acts as a prestressed load. By applying horizontal load separately on the segmental precast, epoxy shear stress is increased by 4–8%, as well as 6–13% for concrete shear stress. The highest horizontal load application is 14.7 kN at K1P6E-NL specimen on 2-stage modeling. Overall from 3 specimens, the maximum force difference between numerical results and previous experiments is from 1 to 28%, while the maximum displacement reaches a difference of up to 40%. The experimental results show a continuous constant trend after the failure of the epoxy. This means that the upper L-shaped block has already touched the lower one. The numerical simulation results proved that the epoxy joint provides brittle failure.